# Properties

 Label 5148.2 Level 5148 Weight 2 Dimension 323872 Nonzero newspaces 120 Sturm bound 2903040

## Defining parameters

 Level: $$N$$ = $$5148 = 2^{2} \cdot 3^{2} \cdot 11 \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$120$$ Sturm bound: $$2903040$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(5148))$$.

Total New Old
Modular forms 735360 327432 407928
Cusp forms 716161 323872 392289
Eisenstein series 19199 3560 15639

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(5148))$$

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space $$S_k^{\mathrm{new}}(N, \chi)$$ we list the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
5148.2.a $$\chi_{5148}(1, \cdot)$$ 5148.2.a.a 1 1
5148.2.a.b 1
5148.2.a.c 1
5148.2.a.d 1
5148.2.a.e 1
5148.2.a.f 1
5148.2.a.g 2
5148.2.a.h 2
5148.2.a.i 2
5148.2.a.j 2
5148.2.a.k 2
5148.2.a.l 3
5148.2.a.m 3
5148.2.a.n 3
5148.2.a.o 3
5148.2.a.p 4
5148.2.a.q 4
5148.2.a.r 4
5148.2.a.s 5
5148.2.a.t 5
5148.2.b $$\chi_{5148}(2287, \cdot)$$ n/a 416 1
5148.2.c $$\chi_{5148}(287, \cdot)$$ n/a 240 1
5148.2.d $$\chi_{5148}(989, \cdot)$$ 5148.2.d.a 48 1
5148.2.e $$\chi_{5148}(1585, \cdot)$$ 5148.2.e.a 2 1
5148.2.e.b 4
5148.2.e.c 8
5148.2.e.d 10
5148.2.e.e 10
5148.2.e.f 24
5148.2.n $$\chi_{5148}(703, \cdot)$$ n/a 360 1
5148.2.o $$\chi_{5148}(1871, \cdot)$$ n/a 280 1
5148.2.p $$\chi_{5148}(2573, \cdot)$$ 5148.2.p.a 56 1
5148.2.q $$\chi_{5148}(133, \cdot)$$ n/a 280 2
5148.2.r $$\chi_{5148}(1717, \cdot)$$ n/a 240 2
5148.2.s $$\chi_{5148}(529, \cdot)$$ n/a 280 2
5148.2.t $$\chi_{5148}(3565, \cdot)$$ n/a 116 2
5148.2.u $$\chi_{5148}(395, \cdot)$$ n/a 672 2
5148.2.w $$\chi_{5148}(2179, \cdot)$$ n/a 700 2
5148.2.y $$\chi_{5148}(109, \cdot)$$ n/a 140 2
5148.2.ba $$\chi_{5148}(2465, \cdot)$$ 5148.2.ba.a 44 2
5148.2.ba.b 44
5148.2.bc $$\chi_{5148}(1873, \cdot)$$ n/a 240 4
5148.2.bh $$\chi_{5148}(2773, \cdot)$$ n/a 120 2
5148.2.bi $$\chi_{5148}(4553, \cdot)$$ n/a 112 2
5148.2.bj $$\chi_{5148}(3851, \cdot)$$ n/a 560 2
5148.2.bk $$\chi_{5148}(3475, \cdot)$$ n/a 832 2
5148.2.bp $$\chi_{5148}(155, \cdot)$$ n/a 1680 2
5148.2.bq $$\chi_{5148}(2419, \cdot)$$ n/a 1728 2
5148.2.br $$\chi_{5148}(329, \cdot)$$ n/a 336 2
5148.2.bs $$\chi_{5148}(1739, \cdot)$$ n/a 1680 2
5148.2.bt $$\chi_{5148}(835, \cdot)$$ n/a 2000 2
5148.2.bu $$\chi_{5148}(857, \cdot)$$ n/a 336 2
5148.2.cd $$\chi_{5148}(725, \cdot)$$ n/a 336 2
5148.2.ce $$\chi_{5148}(1231, \cdot)$$ n/a 2000 2
5148.2.cf $$\chi_{5148}(23, \cdot)$$ n/a 1680 2
5148.2.cg $$\chi_{5148}(1121, \cdot)$$ n/a 336 2
5148.2.ch $$\chi_{5148}(1453, \cdot)$$ n/a 280 2
5148.2.ci $$\chi_{5148}(43, \cdot)$$ n/a 2000 2
5148.2.cj $$\chi_{5148}(419, \cdot)$$ n/a 1680 2
5148.2.cs $$\chi_{5148}(2003, \cdot)$$ n/a 1440 2
5148.2.ct $$\chi_{5148}(571, \cdot)$$ n/a 2000 2
5148.2.cu $$\chi_{5148}(1057, \cdot)$$ n/a 280 2
5148.2.cv $$\chi_{5148}(1517, \cdot)$$ n/a 336 2
5148.2.cw $$\chi_{5148}(815, \cdot)$$ n/a 1680 2
5148.2.cx $$\chi_{5148}(439, \cdot)$$ n/a 2000 2
5148.2.cy $$\chi_{5148}(3301, \cdot)$$ n/a 280 2
5148.2.cz $$\chi_{5148}(2705, \cdot)$$ n/a 288 2
5148.2.de $$\chi_{5148}(3761, \cdot)$$ n/a 112 2
5148.2.df $$\chi_{5148}(3059, \cdot)$$ n/a 560 2
5148.2.dg $$\chi_{5148}(4267, \cdot)$$ n/a 832 2
5148.2.dl $$\chi_{5148}(233, \cdot)$$ n/a 224 4
5148.2.dm $$\chi_{5148}(2107, \cdot)$$ n/a 1440 4
5148.2.dn $$\chi_{5148}(467, \cdot)$$ n/a 1344 4
5148.2.dw $$\chi_{5148}(2393, \cdot)$$ n/a 192 4
5148.2.dx $$\chi_{5148}(181, \cdot)$$ n/a 280 4
5148.2.dy $$\chi_{5148}(415, \cdot)$$ n/a 1664 4
5148.2.dz $$\chi_{5148}(2159, \cdot)$$ n/a 1152 4
5148.2.ea $$\chi_{5148}(463, \cdot)$$ n/a 3360 4
5148.2.ec $$\chi_{5148}(1451, \cdot)$$ n/a 4000 4
5148.2.ef $$\chi_{5148}(241, \cdot)$$ n/a 672 4
5148.2.eh $$\chi_{5148}(89, \cdot)$$ n/a 192 4
5148.2.ej $$\chi_{5148}(353, \cdot)$$ n/a 560 4
5148.2.el $$\chi_{5148}(505, \cdot)$$ n/a 280 4
5148.2.en $$\chi_{5148}(1957, \cdot)$$ n/a 672 4
5148.2.ep $$\chi_{5148}(1541, \cdot)$$ n/a 560 4
5148.2.er $$\chi_{5148}(2243, \cdot)$$ n/a 4000 4
5148.2.et $$\chi_{5148}(1783, \cdot)$$ n/a 1400 4
5148.2.ev $$\chi_{5148}(1255, \cdot)$$ n/a 3360 4
5148.2.ex $$\chi_{5148}(791, \cdot)$$ n/a 1344 4
5148.2.ez $$\chi_{5148}(527, \cdot)$$ n/a 4000 4
5148.2.fb $$\chi_{5148}(67, \cdot)$$ n/a 3360 4
5148.2.fc $$\chi_{5148}(749, \cdot)$$ n/a 560 4
5148.2.fe $$\chi_{5148}(1165, \cdot)$$ n/a 672 4
5148.2.fg $$\chi_{5148}(289, \cdot)$$ n/a 560 8
5148.2.fh $$\chi_{5148}(445, \cdot)$$ n/a 1344 8
5148.2.fi $$\chi_{5148}(157, \cdot)$$ n/a 1152 8
5148.2.fj $$\chi_{5148}(841, \cdot)$$ n/a 1344 8
5148.2.fl $$\chi_{5148}(73, \cdot)$$ n/a 560 8
5148.2.fn $$\chi_{5148}(125, \cdot)$$ n/a 448 8
5148.2.fp $$\chi_{5148}(359, \cdot)$$ n/a 2688 8
5148.2.fr $$\chi_{5148}(775, \cdot)$$ n/a 3328 8
5148.2.fw $$\chi_{5148}(179, \cdot)$$ n/a 2688 8
5148.2.fx $$\chi_{5148}(523, \cdot)$$ n/a 3328 8
5148.2.fy $$\chi_{5148}(17, \cdot)$$ n/a 448 8
5148.2.gd $$\chi_{5148}(25, \cdot)$$ n/a 1344 8
5148.2.ge $$\chi_{5148}(365, \cdot)$$ n/a 1152 8
5148.2.gf $$\chi_{5148}(731, \cdot)$$ n/a 8000 8
5148.2.gg $$\chi_{5148}(1843, \cdot)$$ n/a 8000 8
5148.2.gh $$\chi_{5148}(1609, \cdot)$$ n/a 1344 8
5148.2.gi $$\chi_{5148}(29, \cdot)$$ n/a 1344 8
5148.2.gj $$\chi_{5148}(443, \cdot)$$ n/a 6912 8
5148.2.gk $$\chi_{5148}(259, \cdot)$$ n/a 8000 8
5148.2.gt $$\chi_{5148}(283, \cdot)$$ n/a 8000 8
5148.2.gu $$\chi_{5148}(191, \cdot)$$ n/a 8000 8
5148.2.gv $$\chi_{5148}(425, \cdot)$$ n/a 1344 8
5148.2.gw $$\chi_{5148}(49, \cdot)$$ n/a 1344 8
5148.2.gx $$\chi_{5148}(211, \cdot)$$ n/a 8000 8
5148.2.gy $$\chi_{5148}(1895, \cdot)$$ n/a 8000 8
5148.2.gz $$\chi_{5148}(173, \cdot)$$ n/a 1344 8
5148.2.hi $$\chi_{5148}(545, \cdot)$$ n/a 1344 8
5148.2.hj $$\chi_{5148}(335, \cdot)$$ n/a 8000 8
5148.2.hk $$\chi_{5148}(139, \cdot)$$ n/a 8000 8
5148.2.hl $$\chi_{5148}(101, \cdot)$$ n/a 1344 8
5148.2.hm $$\chi_{5148}(311, \cdot)$$ n/a 8000 8
5148.2.hn $$\chi_{5148}(79, \cdot)$$ n/a 6912 8
5148.2.hs $$\chi_{5148}(575, \cdot)$$ n/a 2688 8
5148.2.ht $$\chi_{5148}(127, \cdot)$$ n/a 3328 8
5148.2.hu $$\chi_{5148}(361, \cdot)$$ n/a 560 8
5148.2.hv $$\chi_{5148}(809, \cdot)$$ n/a 448 8
5148.2.ib $$\chi_{5148}(5, \cdot)$$ n/a 2688 16
5148.2.id $$\chi_{5148}(733, \cdot)$$ n/a 2688 16
5148.2.ie $$\chi_{5148}(167, \cdot)$$ n/a 16000 16
5148.2.ig $$\chi_{5148}(115, \cdot)$$ n/a 16000 16
5148.2.ii $$\chi_{5148}(163, \cdot)$$ n/a 6656 16
5148.2.ik $$\chi_{5148}(479, \cdot)$$ n/a 16000 16
5148.2.im $$\chi_{5148}(215, \cdot)$$ n/a 5376 16
5148.2.io $$\chi_{5148}(427, \cdot)$$ n/a 16000 16
5148.2.iq $$\chi_{5148}(193, \cdot)$$ n/a 2688 16
5148.2.is $$\chi_{5148}(245, \cdot)$$ n/a 2688 16
5148.2.iu $$\chi_{5148}(449, \cdot)$$ n/a 896 16
5148.2.iw $$\chi_{5148}(85, \cdot)$$ n/a 2688 16
5148.2.iy $$\chi_{5148}(145, \cdot)$$ n/a 1120 16
5148.2.ja $$\chi_{5148}(137, \cdot)$$ n/a 2688 16
5148.2.jd $$\chi_{5148}(31, \cdot)$$ n/a 16000 16
5148.2.jf $$\chi_{5148}(83, \cdot)$$ n/a 16000 16

"n/a" means that newforms for that character have not been added to the database yet

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(5148))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(5148)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(44))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(52))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(66))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(78))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(99))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(117))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(132))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(143))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(156))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(198))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(234))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(286))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(396))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(429))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(468))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(572))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(858))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1287))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1716))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2574))$$$$^{\oplus 2}$$